Question

Let R be a relation defined by R = $(a,b):a\ge b,a,bϵR$. The relation R is

• A. Reflexive, symmetric and transitive
• B. Reflexive, transitive but not symmetric
• C. Symmetric, transitive but not reflexive
• D. Neither transitive nor reflexive but symmetric

Answer 1

The correct option is B Reflexive, transitive but not symmetric

$R=(a,b):a⩾b,a,bϵR$

(a) Reflexive because $a⩾a$ will be

true condition

(b) If $a⩾b$

then $b⩾a$ not possible

So, Not symmetric

(c) If $a⩾b$ & $b⩾c$

than it implies $a⩾c$

so, it is transitive.

Hence, the given relation is reflexive,

transitive and not symmetric